Permanent readout superconducting qubit

ABSTRACT

A solid-state quantum computing structure includes a d-wave superconductor in sets of islands that clean Josephson junctions separate from a first superconducting bank. The d-wave superconductor causes the ground state for the supercurrent at each junction to be doubly degenerate, with two supercurrent ground states having distinct magnetic moments. These quantum states of the supercurrents at the junctions create qubits for quantum computing. The quantum states can be uniformly initialized from the bank, and the crystal orientations of the islands relative to the bank influence the initial quantum state and tunneling probabilities between the ground states. A second bank, which a Josephson junction separates from the first bank, can be coupled to the islands through single electron transistors for selectably initializing one or more of the supercurrents in a different quantum state. Single electron transistors can also be used between the islands to control entanglements while the quantum states evolve. After the quantum states have evolved to complete a calculation, grounding the islands, for example, through yet another set of single electron transistors, fixes the junctions in states having definite magnetic moments and facilitates measurement of the supercurrent when determining a result of the quantum computing.

BACKGROUND

1. Field of the Invention

This invention relates to quantum computing and to solid state devicesthat use superconducting materials to create and maintain coherentquantum states such as required for quantum computing.

2. Description of Related Art

Research on what is now called quantum computing traces back to RichardFeynman, [R. Feynman, Int. J. Theor. Phys., 21, 467–488 (1982)]. Feynmannoted that quantum systems are inherently difficult to simulate withconventional computers but that observing the evolution of a quantumsystem could provide a much faster way to solve the some computationalproblems. In particular, solving a theory for the behavior of a quantumsystem commonly involves solving a differential equation related to theHamiltonian of the quantum system. Observing the behavior of the quantumsystem provides information regarding the solutions to the equation.

Further efforts in quantum computing were initially concentrated on“software development” or building of the formal theory of quantumcomputing. Software for quantum computing attempts to set theHamiltonian of a quantum system to correspond to a problem requiringsolution. Milestones in these efforts were the discoveries of the Shorand Grover algorithms. [See P. Shor, SIAM J. of Comput., 26:5, 1484–1509(1997); L. Grover, Proc. 28th STOC, 212–219 (1996); and A. Kitaev, LANLpreprint quant-ph/9511026 (1995)]. In particular, the Shor algorithmpermits a quantum computer to factorize natural numbers. The showingthat fault-tolerant quantum computation is theoretically possible openedthe way for attempts at practical realizations of quantum computers.[See E. Knill, R. Laflamme, and W. Zurek, Science, 279, p. 342 (1998).]

One proposed application of a quantum computer is factoring of largenumbers. In such an application, a quantum computer could renderobsolete all existing encryption schemes that use the “public key”method. In another application, quantum computers (or even a smallerscale device, a quantum repeater) could allow absolutely safecommunication channels, where a message, in principle, cannot beintercepted without being destroyed in the process. [See H. J. Briegelet al., LANL preprint quant-ph/9803056 (1998) and the referencestherein.]

Quantum computing generally involves initializing the states of N qubits(quantum bits), creating controlled entanglements among the N qubits,allowing the quantum states of the qubits to evolve under the influenceof the entanglements, and reading the qubits after they have evolved. Aqubit is conventionally a system having two degenerate quantum states,and the initial state of the qubit typically has non-zero probabilitiesof being found in either degenerate state. Thus, N qubits define aninitial state that is a combination of 2^(N) degenerate states. Theentanglements control the evolution of the distinguishable quantumstates and define calculations that the evolution of the quantum statesperforms. This evolution, in effect, performs 2_(N) simultaneouscalculations. Reading the qubits after evolution is complete determinesthe states of the qubits and the results of the calculations.

Several physical systems have been proposed for the qubits in a quantumcomputer. One system uses chemicals having degenerate spin states.Nuclear magnetic resonance (NMR) techniques can read the spin states.These systems have successfully implemented the Shor algorithm forfactoring of a natural number (15). However, efforts to expand suchsystems up to a commercially useful number of qubits face difficultchallenges.

Another physical system for implementing a qubit includes asuperconducting reservoir, a superconducting island, and a dirtyJosephson junction that can transmit a Cooper pair (of electrons) fromthe reservoir into the island. The island has two degenerate states. Onestate is electrically neutral, but the other state has an extra Cooperpair on the island. A problem with this system is that the charge of theisland in the state having the extra Cooper pair causes long rangeelectric interactions that interfere with the coherence of the state ofthe qubit. The electric interactions can force the island into a statethat definitely has or lacks an extra Cooper pair. Accordingly, theelectric interactions can end the evolution of the state beforecalculations are complete or qubits are read. This phenomenon iscommonly referred to as collapsing the wavefunction, loss of coherence,or decoherence.

Research is continuing and seeking a structure that implements a quantumcomputer having a sufficient number of qubits to perform usefulcalculations.

SUMMARY

In accordance with the invention, a qubit includes a superconductingisland that a Josephson junction separates from a superconducting bank.The island has a crystal orientation that differs from the crystalorientation of the reservoir, and a grain boundary between the islandand reservoir forms a clean (ballistic) Josephson junction. One or bothof the island and the bank are D-wave superconductors so that a groundstate current flows at the Josephson junction. The ground state of thesupercurrent at the Josephson junction is twice degenerate with themagnetic moment produced by the supercurrent distinguishing the twostates. The crystal orientation of the island relative to the bankcontrols the equilibrium phase difference in the order parameter acrossthe junction and therefore the tunneling probabilities between theground states.

To read the supercurrent state associated with the island, a singleelectron transistor (SET) or parity key can connect the island toground. When the SET is biased to conduct, the current through the SETcollapses supercurrent state to a state with fixed magnetic moment andfixes the supercurrent in that state. Thus, upon completion of acalculation, a control circuit biases the SET to conduct, and themagnetic moment at the Josephson junction is fixed in a particular stateand can be dependably read.

To form a quantum register, multiple Josephson junctions can couplerespective superconducting islands to a superconducting bank, and acurrent through the bank can initialize the quantum states of thesupercurrents at the junctions. Single electron transistors (SETs) orparity keys interconnect the islands to create controlled entanglementsas required for quantum computing. After completion of the computing,other SETs or parity keys connect the islands to ground and freeze thesupercurrents at the Josephson junctions into states having definitemagnetic moments. This freezing maintains the states for subsequent readoperations that measure the local magnetic moments or magnetic flux.

One embodiment of the invention is a quantum computing structure such asa quantum coherer or a quantum register that includes a bank of asuperconducting material and an island of a superconducting material,wherein at least one of the island and the bank is a d-wavesuperconductor. The normal-conductor portion of a clean Josephsonjunction can be, for example, a grain boundary between the bank and theisland. Optionally, a single electron transistor (SET) or a parity keyis between the island and ground. The orientation of the supercurrentthrough the junction is fixed when the SET is conductive and can evolvewhen the SET is non-conductive. As another option, the structure alsoincludes a second bank of superconducting material, and a Josephsonjunction between the first and second banks. Operation of a SET betweenthe second bank and the island selectively initializes thesupercurrent's quantum state according to the phase of the orderparameter in the first or second bank.

Another embodiment of the invention is a quantum register that includes:a bank of a superconducting material; a plurality of islands ofsuperconducting material; and a plurality of clean Josephson junctions.Each clean Josephson junction is between the bank and a correspondingone of the islands. One or both of the island and the bank include ad-wave superconductor. The quantum register optionally includes threesets of SETs. Each SET in a first set is between ground and acorresponding one of the islands. Each SET in the second set is betweena corresponding pair of the islands. Each SET in the third set isbetween a second bank and a corresponding one of the islands. TheJosephson junction creates an order parameter phase difference betweenthe first and second banks. The second bank and the third set of SETscan be used for selective initialization of supercurrents at thejunctions according to the phase of the second bank.

In accordance with another embodiment of the invention, a quantumcomputing method cools a structure including a bank and an island to atemperature that makes the bank and the island superconducting andsuppresses the decoherence processes in the system. The structureincludes a junction that is a clean Josephson junction between theisland and the bank. After the structure is at the appropriatetemperature, the method establishes a supercurrent at the junction in aquantum state that is an admixture of a first state having a firstmagnetic moment and a second state having a second magnetic moment. Thesupercurrent at the junction is a ground state current arising from useof a d-wave superconductor in the structure and can be set by running acurrent through the bank. The quantum state evolves according toprobabilities for tunneling between the first and second ground states.The evolution performs the quantum computing. Determining a measuredmagnetic moment or flux due to the supercurrent at the junctiondetermines a result from the quantum computing.

In accordance with another aspect of the invention, determining themeasured magnetic moment includes: grounding the island to fix thesupercurrent in the first or second state; and measuring the magneticflux produced by the supercurrent while the island is grounded.

Typically, the quantum register further includes a plurality of islandsand a plurality of junctions, each junction being a clean Josephsonjunction between the bank and a corresponding island. The quantum statesof the supercurrents at the junctions evolve according to theconductivities of transistors that couple islands together. Thesetransistors create entanglements of the quantum states of the islands.The manufacturer of the quantum register can select for each island, acrystal orientation according to the initial quantum state desired forthe island.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A, 1B, and 1C are plan views of quantum coherer having ahorizontal architecture in accordance with an embodiment of theinvention.

FIGS. 2A, 2B, and 2C are cross-sectional views of horizontal quantumcoherers that in accordance with embodiments of the invention.

FIGS. 3A and 3B are respectively plan and cross-sectional views of avertical quantum coherer in accordance with an embodiment of theinvention.

FIGS. 4A and 4B are respectively plan and cross-sectional views of avertical quantum coherer in accordance with another embodiment of theinvention.

FIG. 5 is cross-sectional views of a hybrid vertical/horizontal quantumcoherer in accordance with an embodiment of the invention.

FIG. 6 shows a qubit having a single electron transistor that freezesthe state of the qubit.

FIG. 7 shows a structure including a collection of qubits having singleelectron transistors that create entanglements among the qubits andfacilitate read out of the qubits.

FIG. 8 illustrates a system having a double bus capable of applyingdifferent phases of the order parameter from the buses to the qubit.

Use of the same reference symbols in different figures indicates similaror identical items.

DETAILED DESCRIPTION

In accordance with an aspect of the invention, quantum computing usesqubits based on the degenerate ground states of the supercurrent at aDD, DND, or SND Josephson junction. The Josephson junctions can befabricated in useful numbers in a solid state structure. With a d-wavesuperconductor on at least one side of the Josephson junction, theJosephson junction has non-zero ground state supercurrent in thevicinity of the junction. This ground state supercurrent is eitherclockwise or counterclockwise in the preferred (so called ab-) plane ofthe d-wave superconductor. The ground-state supercurrent in the vicinityof each Josephson junction is thus doubly degenerate and provides thebasis for a quantum coherer or a qubit for quantum computing inaccordance with an embodiment of the invention.

FIG. 1A is a plan view of horizontal quantum coherers 100 in accordancewith exemplary embodiments of the invention. Quantum coherer 100provides a basic block for construction of a qubit but can also be anindependent device allowing demonstration of macroscopic quantumtunneling and incoherent quantum noise in a solid state system. Asdescribed further below, the macroscopic quantum tunneling in a set ofindependent quantum coherers permits construction of a random numbergenerator that generates random series with zero correlation.

Quantum coherer 100 includes a Josephson junction 130 between a largesuperconducting bank 110 and a mesoscopic, superconducting island 120formed on an insulating substrate 140. At least one of bank 110 andisland 120 is a d-wave superconductor, for example, a high-Tc cupratesuch as YBa₂Cu₃O_(7-x) or any superconductor, in which the Cooper pairsare in a state with non-zero orbital angular momentum. In a firstexemplary embodiment of the invention, both bank 110 and island 120 aremade of a d-wave superconductor. In this embodiment, junction 130 isclean in that the junction is conducting (e.g., a normal conductinglayer or a grain boundary) and lacks scattering cites. As describedfurther below, a grain boundary between a d-wave superconductor bank 110and a d-wave superconductor island 120 can create Josephson junction130.

In a second exemplary embodiment, bank 110 is an s-wave superconductingmaterial such as Niobium (Nb), and island 120 is a d-wavesuperconductor. In a third embodiment, bank 110 is a d-wavesuperconducting material, and island 120 is an s-wave superconductor.For the second and third embodiments, junction 130 includes a normalconductor between bank 110 and island 120. The normal conductor can beany conductive material that forms a good contact with both the d-waveand s-wave superconductors, has a large elastic scattering length, andremains a normal conductor at the operating temperature of quantumcoherer 100 (typically between about 10°K and about 1°K). In particular,gold (Au) is a suitable normal conductor for junction 130.

In the exemplary embodiments, bank 110 is a chip of superconductingmaterial about 1 μm or more in length and width. The thickness of bank110 is not critical but generally should not exceed that of themesoscopic island 120. Island 120 is mesoscopic (i.e., has a size suchthat a single excess Cooper pair is noticeable) and typically has awidth W about 0.2 μm or less, a length L about 0.5 μm or less, andthickness about 0.2 μm or less.

The term mesoscopic, in general, refers to

a class of solid systems where the single particle approach holds andgives sensible results, namely, the mesoscopic systems (see, e.g., Imry1986). These are systems of intermediate size, i.e., macroscopic butsmall enough (10⁻⁴ cm). In these systems quantum interference is veryimportant, since at low enough temperatures (<1K) the phase coherencelength of quasiparticles (“electrons”) exceeds the size of the system.This means that the electrons preserve their “individuality” whenpassing through the system.

Since the wave function of the quantum particle depends on its energy ase^(iET), any inelastic interaction spoils the phase coherence. Then thecondition1_(φ)1₁ <L[sic] (1.53)

-   -   must hold. Here 1_(φ) is the phase coherence length, 1_(i) is        the inelastic scattering length, L is the size of the system.        The above condition can be satisfied in experiment, due to the        fact we have discussed above: that in the condensed matter we        can deal with weakly interacting quasiparticles instead of        strongly interacting real particles.

Because the inelastic scattering length of the quasielectron exceeds thesize of the mesoscopic system, we can regard it as a single particle inthe external potential field and apply to it the path integral formalismin the simplest possible version.

-   Alexander M. Zagoskin, QUANTUM THEORY OF MANY-BODY SYSTEMS p. 19–20    (Springer 1998), citing Y. Imry, “Physics of Mesoscopic Systems,” in    DIRECTIONS IN CONDENSED MATTER PHYSICS: MEMORIAL, VOLUME IN HONOR OF    SHANG-KENG MA (ed. G. Grinstein, G. Mazenko, World Scientific 1986).

Quantum coherer 100 can be formed using conventional techniques. In thefirst exemplary embodiment where both bank 110 and island 120 are d-wavesuperconductors, substrate 140 is a bi-crystal substrate such as astrontium-titanate bi-crystal substrate available from KagakuGijutsu-shaof Tokyo, Japan. The fabrication process begins by growing a film of ahigh-Tc cuprate having a thickness of about 0.2 microns on substrate140. Regions of the high-Tc cuprate film inherit different crystalorientation from underlying substrate 140, and a grain boundary formsbetween the two different regions. Such a film can be grown using pulsedlaser deposition, which uses a laser beam to sputter the high-Tc cuprateonto substrate 140. A photolithographic process then masks and etchesthe film to form island 120 (typically as one of several islands)adjacent bank 110. For islands 120 of the small size desired, theetching or patterning process can use an electron beam to remove part ofthe d-wave superconductor and leave island 120 with the desireddimensions. II'ichev et al., cond-mat/9811017, p. 2 describes knownfabrication technique using high-Tc cuprates and is hereby incorporatedby reference in its entirety.

In the second and third embodiments where one of bank 110 or island 120is an s-wave superconductor, the fabrication process starts bydepositing a film of d-wave superconductor on substrate 140. The film isetched (if necessary) to limit the boundaries of the d-wavesuperconductor to the desired boundaries of bank 110 or island 120.Alternatively, bank 110 or island 120 can be etched from a bulk d-wavefilm. A normal conductor such as gold is deposited and patterned toleave material for junctions 130. Finally, a film of s-wavesuperconductor is deposited and patterned (if necessary) to limit theboundaries of the s-wave superconductor for bank 110 or island 120.

For operation, quantum coherer 100 is cooled to a temperature less thanabout 10°K so that bank 110 and island 120 are superconducting andJosephson junction 130 is operative. The operating temperature ofquantum coherer 100 is far below the threshold temperature forsuperconductivity of the d-wave superconductor to suppress thermalsources of decoherence. In particular, the low temperature suppressesdecoherence processes due to inelastic scattering. If quantum coherer100 contains an s-wave superconductor, the operating temperature isbelow the transition temperature of the s-wave superconductor (e.g.,below 9.25°K for pure Nb).

At junction 130, the d-wave superconductor causes a non-zerosupercurrent in the ground state, and the ground state of thesupercurrent is twice degenerate if no external electromagnetic field isapplied. Two degenerate states having the ground state energy anddefinite magnetic moment correspond to minimal supercurrents circulatingthrough Josephson junction 130 in clockwise and counter-clockwisesenses, in a preferred plane of the crystal structures of bank 110and/or island 120. In accordance with current theoretical descriptions,e.g., the Ginzburg-Landau theory, of superconductivity, an orderparameter T describes supercurrents in superconductors, and a phasedifference Δφ in the order parameter when crossing junction 130indicates the state or direction of the supercurrent. The two statesassociated with the supercurrent in island 120 permit quantum computingas described further below.

Quantum coherer 100 operates at a temperature below about 10°K so thatbank 110 and island 120 are superconducting and thermal excitations donot interfere with the coherence of the quantum state associated withthe supercurrent in island 120. An external circuit (not shown) cangenerate an electric field that causes a current through bank 110 to theright or left that initializes quantum coherer 100 to a quantum statecorresponding to a known superposition of the clockwise andcounterclockwise supercurrent states at junction 130. Alternatively,temporary application of a magnetic field can also initialize the stateof island 120 by temporarily breaking the degeneracy in the two groundstate energies. Subsequent quantum tunneling between the ground statescauses the state of island 120 to evolve.

In the first exemplary, island 120 is a d-wave superconductor with acrystal orientation that differs from that of bank 130. Since theJosephson junction is a clean junction, the difference in crystalorientation is a primary factor in determining the magnitude of theequilibrium phase difference Δφ in the order parameter Ψ at thejunction, and the magnitude of the phase difference Δφ is not restrictedto π/2 as typically would be the case with a tunneling junction. (Thetwo degenerate states of the junction respectively correspond topositive and negative phase differences Δφ.) Accordingly, the choice oflattice mismatch between bank 110 and island 120 selects the phasedifference Δφ. This permits selection of tunneling rates between theground states within an exponentially wide range.

Another advantage of having a clean junction is a difference in crystalorientations (or Δφ) can restrict the ground states to having a lowprobability of being in states having excess charge on island 120. Thus,the state of island 120 has weaker electrostatic interactions with thesurroundings. This reduces or eliminates a source of decoherence in thestate of island 120, and the state of island 120 can continue to evolvefor a relatively long period without collapsing the wavefunction. Thespontaneous supercurrent at Josephson junction 130 creates spontaneousmagnetization, and the direction of the current and the magnetizationdistinguish the working quantum states of quantum coherer 100. However,the magnetic reactions with the surroundings are weak enough to avoidsignificant problems with decoherence.

The geometry or architecture of Josephson junction 130 in quantumcoherer 100 can be varied in variety of ways that facilitate selectionof the phase difference Δφ in the superconducting order parameter. FIG.1B is a plan view of a quantum coherer 100B according to anotherembodiment of the invention. Quantum coherer 100B includes a Josephsonjunction 130B that separates bank 110 from mesoscopic island 120.Josephson junction 130B is particularly suited for the embodiments ofthe invention where one of bank 110 and island 120 is an s-wavesuperconductor and the other one of bank 110 and island 120 is a d-wavesuperconductor. Bank 110, island 120, and junction 130B are respectivelyformed in the same manner described above for bank 110, island 120, andjunction 130 of FIG. 1A.

Quantum coherer 100B differs from quantum coherer 100 in crystalorientation of island 120 relative to bank 110 across junction 130B. Thea-b plane of the d-wave superconductor lies in the plane of FIG. 1B. Incoherer 100B, junction 130B has three regions S1, S2, and S3 where therelative crystal orientation of bank 110 and island 120 across region S1differs from the relative crystal orientation across regions S2 and S3.The lengths of regions S1, S2, and S3 can be changed to adjust theequilibrium phase difference in the superconducting order parameteracross junction 213 and the magnitude of the magnetic flux of the groundstate supercurrent.

FIG. 1C shows a plan view of another horizontal quantum coherer 100C inwhich a Josephson junction 130C has two regions S1 and S2 with differentcrystal orientations across the regions S1 and S2. As in coherer 1001B,changing the orientation of island 120 and the lengths of regions S1 andS2 can adjust the phase difference in the superconducting orderparameter between bank 110 and island 120.

The cross-section of the junction 130 also has several alternativeconfigurations. FIG. 2A shows a cross-sectional view of a horizontalquantum coherer where both bank 110 and island 120 are d-wavesuperconductors and a grain boundary forms Josephson junction 130. FIG.2B shows a cross-sectional view of a horizontal quantum coherer where anormal conductor between bank 110 and island 120 forms Josephsonjunction 130. The normal conductor is suitable when both bank 110 andisland 120 are d-wave superconductors or when one of bank 110 and island120 is an s-wave superconductor.

FIG. 2C illustrates that surface of the Josephson junction 130 is notrequired to be perpendicular to the preferred plane (the ab-plane) ofthe supercurrent in the d-wave superconductor. Current techniques forgrowing a high-Tc superconductor on insulating substrate 140 typicallykeep the ab-plane of the high-Tc superconductor substantially parallelto the surface of substrate 140. In FIG. 2C, junction 130 is at an anglerelative to the c-direction of the d-wave superconductor. Normally, thedeposition of the d-wave superconductor film on substrate 140 keeps theab-plane of the d-wave superconductor parallel to the surface ofsubstrate 140 and the c-direction perpendicular to the surface.Conventional patterning of the film creates an edge parallel to thec-direction. However, an anisotropic etch process such as electron beametching with substrate 140 at an angle to the beam direction can createa non-zero angle between the edge of the d-wave film and thec-direction. This angle provides another degree of freedom in selectinga configuration that provides the desired phase difference Δφ in thesuperconducting order parameter.

FIGS. 3A and 3B respectively show a plan view and a cross-sectional viewof a vertical quantum coherer 300 in accordance with an embodiment ofthe invention. The terms “horizontal” and “vertical” as applied to thequantum coherers described herein indicate the predominant plane of theground state supercurrents. Quantum coherer 300 includes an insulatingsubstrate 340, a superconducting bank 310, a Josephson junction 330, anda mesoscopic superconducting island 320. A fabrication process forquantum coherer 300 grows a d-wave superconductor film to a thicknessbetween about 0.2 μm and about 0.5 μm on substrate 340. Deposition of anormal conductor such as gold on the d-wave superconductor film forms anormal conductor film between about 0.1 μm and about 0.3 μm thick.Deposition of an s-wave superconductor such as Nb on the normalconductive film forms an s-wave superconductor film less than about 0.2μm thick. Finally, patterning of the s-wave superconductor film and thenormal conductor film creates mesoscopic, superconductive island 320that Josephson junction 330 separated from superconductive bank 310.

FIGS. 4A and 4B respectively show plan and cross-sectional views of aquantum coherer 400 having a vertical architecture according to anotherembodiment of the invention. Quantum coherer 400 includes asuperconductor bank 410, a mesoscopic superconductor island 420, and aJosephson junction 430, formed on an insulating substrate 440. Afabrication process for quantum coherer 400 grows a d-wavesuperconductor film on substrate 440 to a thickness less than about 0.2μm and patterns the film to form island 420. Insulative sidewall spacers450 are then formed on island 420. Such spacers can be conventionallyformed by depositing and patterning an insulative layer or by aself-aligned process that anisotropically etches a conformal insulativelayer formed on substrate 440 and island 420. A layer of a normalconductor such as gold is deposited on the resulting structure to athickness between about 0.1 μm and about 0.3 μm and patterned to form anormal conductive region of Josephson junction 430. The normalconductive region extends over island 420 and at least part of sidewallspacers 440. Finally, a layer of an s-wave superconductor is depositedon the structure and patterned (if necessary) to form bank 410. Thethickness of bank 410 is not critical to the operation of quantumcoherer 400.

FIG. 5 shows a cross-sectional view of a quantum coherer 500 having ahybrid vertical/horizontal architecture according to another embodimentof the invention. Quantum coherer 500 includes a superconductor bank510, a mesoscopic superconductor island 520, and a Josephson junction530, formed on an insulating substrate 540. A fabrication process forquantum coherer 500 grows a d-wave superconductor film on substrate 440to a thickness less than about 0.2 μm and patterns the film to formisland 520. The patterning can leave sides of island 520 perpendicularto the surface of substrate 540 or any desired angle. A layer of anormal conductor such as gold is deposited on the resulting structure toa thickness between about 0.1 μm and about 0.3 μm and patterned to forma normal conductive region of Josephson junction 530. In thisembodiment, the normal conductive region extends over island 520 and isin contact with at least one sidewall of island 520. Finally, a layer ofan s-wave superconductor is deposited on the structure and patterned (ifnecessary) to form bank 510. The phase difference in the superconductingorder parameter from bank 510 to island 520 depends on the relativecrystal orientation between the top surface of island 520 and theoverlying part of bank 510 and the relative crystal orientation of theside of island 520 and the adjacent part of bank 510.

The quantum coherers such as described above avoid the destructiveeffects of low energy thermal excitations for several reasons. Inparticular, the superconducting gap (between the ground state energy ofCooper pairs and the higher energy states of electrons) and the smallphase volume available in the nodes of the d-wave order parameter in thesuperconducting island and the bank suppress the low energy elementaryexcitations. Moreover, near the boundary, there is a possibility ofspecific admixture of s-wave superconductivity restoring the finiteenergy gap on all of the Fermi surface. In a normal layer of thejunction, where the order parameter is suppressed, the elementaryexcitations are gapped due to size quantization.

One application of the quantum coherers is in a random number generator.In this application, the quantum states of a set of quantum coherersevolve to a state where each quantum coherer has an equal (or at leastknown) probability of being in each of the current direction states. Thecurrent-directions states are then determined, for example, by observingeach quantum coherer with a magnetic force microscope or anothermagnetic probe. Each determined state (clockwise or counterclockwise)corresponds to a bit value (0 or 1) so that the collection of determinedstates provides a random binary value having as many bits as there arequantum coherers in the set. Quantum theory indicates that a series ofbits thus generated are random without correlation or repetition.

FIG. 6 shows an embodiment of a qubit 600 based on the architecture ofquantum coherer 100. Qubit 600 is merely an illustrative embodiment of aqubit in accordance with the invention, and other embodiments of qubitcan employ other quantum coherer architectures such as but not limitedto those described above.

Qubit 600 combines quantum coherer 100 with external circuitry thatallows freezing of the quantum tunneling between the two degeneratesupercurrent ground states. To freeze the quantum state of thesupercurrent, a parity key or single electron transistor (SET) 640connects island 120 to ground (normal or superconducting). The freepassage of electrons between island 120 and ground collapses thewavefunction of the supercurrent at junction 130 into one of the groundstates (a state corresponding to either phase difference Δφ or −Δφ)having definite magnetic moment. (The probability of collapsing to aparticular phase difference Δ+ or −Δφ depends on probability amplitudesin the ground state before the collapse.) Island 120 remains in thedefinite magnetic moment state while SET 640 continues to connect island120 to ground, and that state, while frozen, can be measured to read outand determine the results of a calculation. Changing the gate voltage ofSET 640 can stop the flow of electrons to or from ground and therebyallows island 120 to evolve according to the tunneling rate between theground states.

Single electron transistors are known and described, for example, by A.Zagoskin, “Quantum Theory of Many-Body Processes”, which is herebyincorporated by reference in its entirety. SETs include a graincapacitively coupled to two devices (e.g., island 120 and ground). Anelectron or Cooper pair can tunnel from either device onto the grainwhen the grain is uncharged. However, the grain is small enough thatonce an electron or Cooper pair tunnels onto the grain, the charging ofthe grain electrically repels and prevents further tunneling onto thegrain. A gate associated with the grain can change the voltage of grainto shut off or otherwise control the tunneling rate. P. Joyez et al.,“Observation of Parity-Induced Suppression of Josephson Tunneling in theSuperconducting Single Electron Transistor”, Physical Review Letters,Vol. 72, No. 15, 11 April 1994 describes operation and manufacture ofsingle electron transistors and is also incorporated by reference hereinin its entirety.

Joyez et al., Observation of Parity-Induced Suppression of JosephsonTunneling in the Superconducting Single Electron Transistor, Phys. Rev.Lett. 72, pp. 2458–2461, provide a complete description of the operationof a superconducting single electron transistor (SET). Joyez et al.states that:

The consequences of the duality of phase and number-of-particlevariables are particularly well illustrated by the competition betweenJosephson tunneling and single electron charging phenomena in ultrasmallsuperconducting junction systems. One of the simplest devices consistsof two Josephson junctions in series: The number of Cooper pairs on themiddle “island” tends to be fixed by the charging energy E_(c)=e²/2C ofthe island while the associated phase tends to be fixed by the Josephsoncoupling energy E_(J) of the two junctions which we suppose identicalfor simplicity. Here C refers to the total capacitance of the island.This model system has been investigated theoretically in detail. Forlarge area junctions (E_(J)>>E_(C)) the charging effects are overcome byJosephson tunneling and the maximum supercurrent that can flow throughthe two junction system is just I_(O)=2eE_(J)/, the maximum supercurrentof each junction. However, for small area junctions (E_(J)<<E_(C)), themaximum supercurrent should strongly depend on the polarization chargeQ_(g) applied to the island by means of a gate electrode, hence the nameof “superconducting single electron transistor” given to such a device.

(Joyez et al., p. 2458). Further, Joyez et al. describe fabrication of aSET:

The sample was prepared using standard e-beam lithography and shadowmask evaporation techniques. The main difference with previousexperiments is the use of the three-angle evaporation technique ofHaviland et al., J. Phys. B 85, 339 (1991) in order to fabricate in asingle pump down the alumina-covered Al island electrode, the two Aldrain and source electrodes, and the Cu (3 wt. % Al) buffer electrodes.

(Joyez et al., p. 2458) (citation added). With regard to Parity Keys,ZAGOSKIN, p. 206, describes the parity effect in the following passage:

If the grain becomes superconducting, there appear interesting newpossibilities. As we know, in the ground state of a superconductor allelectrons are bound in Cooper pairs (and therefore the ground state cancontain only an even number of electrons). Any odd electron will thusoccupy an excited state, as a bogolon, and its minimum energy, measuredfrom the ground state energy, will be Δ.

This is the parity effect in superconductivity. Of course, in a bulksuperconductor it is of no importance, but not so in our small system,where charging effects enter the game.

Qubit 600 is referred to herein as a permanent readout superconductingqubit (PRSQ) because barring thermal fluctuations, the spontaneousmagnetic flux of a frozen (grounded and collapsed) qubit remains fixed.Accordingly, a readout device such as a magnetic force microscope (MFM)tip or a superconducting quantum interferometer device (SQUID) loop cancontact the system when the decohering effects of the read out devicewill not disrupt the qubit result. The readout device measures the weaklocal magnetic fields that the spontaneous supercurrents (clockwise orcounterclockwise) cause in the vicinity of the Josephson junction 120.More particularly, the MFM scans a microscopic magnetized tip attachedto a cantilever across the surface and measures deformation of thecantilever as the mechanical force that acts on the magnetized tip.Alternatively, a SQUID loop detects the magnetic flux in the vicinity ofthe Josephson junction 130. Another possible read out system may use adifference in the absorption of circularly polarized microwave radiationdue to the clockwise or counterclockwise currents at the junction.

FIG. 7 shows a PRSQ register 700 including several islands 120-1 to120-N in contact with a bank 110. In the exemplary embodiment, islands120-1 to 120-N and bank 110 are made of a d-wave superconductor at atemperature of about 10° K as described above. Grain boundaries arebetween bank 110 and respective islands 120-1 to 120-N and form cleanJosephson junctions 130-1 to 130-N, respectively. The crystalorientations of islands 120-1 to 120-N differ from the crystalorientation of bank 110 and control equilibrium phase differences Δφ₁ toΔφ_(N) between the phase of the order parameter in bank 110 and thephases of the order parameter in islands 120-1 to 120-N. Phases Δφ₁ toΔφ_(N) can differ from each other or all be the same. A manufacturer ofPRSQ register 700 selects phases Δφ₁ to Δ+_(N) according to theapplication of register 700 and designs a substrate that will create thedesired grain boundaries when d-wave superconductive material isdeposited on the substrate.

To facilitate readout from PRSQ register 700. SETs 640-1 to 640-N arebetween islands 120-1 to 120-N and ground. Turning on SETs 640-1 to640-N permits free current between ground and respective islands 120-1to 120-N to collapse and freeze the quantum states of the supercurrentsat respective junctions 130-1 to 130-N. The techniques described abovecan then read the quantum states.

Register 700 also includes SETs 750-2 to 750-N that connect adjacentislands 120-1 to 120-N. Voltages applied to the gates of SETs 750-2 to750-N control currents or tunneling probabilities between islands andthereby create controllable entanglements among the quantum states ofsupercurrents in register 700.

In FIG. 7, islands 120-1 to 120-N are in a linear array, and each island120-2 to 120-N has a corresponding SETs 750-2 to 750-N that connects tothe respective preceding islands 750-1 to 750-(N−1) in the linear array.Alternative configurations are possible, for example, an additional SETcan connect island 120-1 to island 120-N in a ring. In anotherembodiment, each island connects through multiple SETs to other islands,for example, in a two-dimensional array of qubits. The configuration andconnections of islands can be selected according to the function of orprogram for PRSQ register 700.

To execute quantum computing with PRSQ register 700, the states of thequbits corresponding to islands 120-1 to 120-N are first initialized inthe same manner as described above, for example, by running a currentthrough bank 110. All of SETs 640-1 to 640-N are off to preventinteraction with ground, and the voltages on the gates of SETs 750-2 to750-N are adjusted according to the desired calculation. SETs 750-2 to750-N create entanglements that enable tunneling between the groundstates of PRSQ register 700. After the quantum state of PRSQ register700 evolves to complete the desired calculation, SETs 750-2 to 750-N areturned off to decouple the qubits, and then SETs 640-1 to 640-N areturned on. This collapses the wavefunction so that the supercurrent ateach Josephson junction 130-1 to 130-N has a definite magnetic moment.One or more read out devices sense the magnetic moments of thesupercurrents at junctions 130-1 to 130-N to determine the results ofthe quantum computing.

The time required for a calculation and the interpretation of the readout results depends on the calculation performed. Such issues are thesubject of many papers on quantum computing. The structures describedherein can perform such calculations provided that the structuresprovide a sufficeint number of qubits and a decoherence time that islonger than the required calculation time. The structures can typicallyachieve longer coherence times by decreasing the operating temperature.

FIG. 8 illustrates a quantum register 800 having a double busconfiguration. Quantum register 800 includes a first superconductingbank 110 and a second superconducting bank 810 with a Josephson junction830 between the banks. Josephson junction 830 creates a phase differenceΔφ between the order parameter in bank 110 and the order parameter inbank 120. Josephson junction 830 is preferably a clean Josephsonjunction so that phase difference Δφ depends on the relative crystalorientations of banks 110 and 120, but junction 830 is alternatively aninsulative or dirty Josephson junction. Superconducting islands 120-1 to120-N connect to bank 110 via respective clean Josephson junctions 130-1to 130-N.

Quantum register 800 includes three sets of SETs. SETs 640-1 to 640-Nconnect to respective islands 120-1 to 120-N to ground. SETs 750-2 to750-N connect adjacent islands for controlled entanglements. SETs 840-1to 840-N are between respective islands 120-1 to 120-N and bank 810. Anadvantage of quantum register 800 is the ability to change theinitialization and ground-state tunneling probabilities by selectingwhich, if any, of SETs 840-1 to 840-N connect corresponding islands120-1 to 120-N to bank 810.

To illustrate an initialization process using double-bus quantumregister 800, let the phase of the superconducting order parameter inbus 110 be zero. The relative phase χ of bus 810 can be created byconnecting bus 110 and 810 on the left of FIG. 8 and passing an externalmagnetic field through the left most portion of the resulting loop.Opening selected keys 840-1 to 840-N (while keys 640-1 to 640-N remainclosed) creates an energy difference between the two previouslydegenerate ground states in the corresponding islands 120-1 to 120-N. Inparticular, the states with phases +Δφ and −Δφ when connected to bus 810differ in energy with the energy difference being proportional to[cos(Δφ+χ)-cos(Δφ-χ)]. The connected islands 120-1 to 120-N eventuallysettle to the lowest energy state +Δφ or −Δφ depending on the phase χ ofbus 810.

Although the invention has been described with reference to particularembodiments, the description is only an example of the invention'sapplication and should not be taken as a limitation. Various adaptationsand combinations of features of the embodiments disclosed are within thescope of the invention as defined by the following claims.

1. A quantum computing structure comprising: a first bank of a superconducting material having a first crystal orientation; a mesoscopic island of a superconducting material having a second crystal orientation, wherein at least one of the island and the bank comprises a d-wave superconducting material; and a clean Josephson junction between the island and the bank.
 2. The structure of claim 1, further comprising a single electron transistor connected between the island and ground.
 3. The structure of claim 1, wherein the clean Josephson junction comprises a grain boundary between the bank and the island.
 4. The structure of claim 1, wherein the island comprises a d-wave superconducting material.
 5. The structure of claim 4, wherein the bank comprises a d-wave superconducting material.
 6. The structure of claim 1, further comprising: a second bank of superconducting material having a third crystal orientation; and a Josephson junction between the first and second banks.
 7. The structure of claim 6, further comprising a single electron transistor coupled between the second bank and the island.
 8. A quantum register comprising: a bank of a superconducting material; a plurality of mesoscopic islands of superconducting material; and a plurality of clean Josephson junctions, each clean Josephson junction being between the bank and a corresponding one of the islands, wherein at least one of the plurality of mesoscopic islands and the bank comprises a d-wave superconducting material.
 9. The quantum register of claim 8, further comprising a plurality of single electron transistors, each electron transistor being between ground and a corresponding one of the islands.
 10. The quantum register of claim 8, further comprising a first plurality of single electron transistors, each single electron transistor in the first plurality being between islands in a corresponding pair of the islands.
 11. The quantum register of claim 10, further comprising a second plurality of single electron transistors, each single electron transistor in the second plurality being between ground and a corresponding one of the plurality of mesoscopic islands.
 12. The quantum register of claim 8, further comprising: a second bank of superconducting material; and a Josephson junction between the first and second banks.
 13. The quantum register of claim 12, further comprising a first plurality of single electron transistors, each single electron transistor being coupled between the second bank and a corresponding one of the islands.
 14. The quantum register of claim 13, further comprising a second plurality of single electron transistors, each single electron transistor in the second plurality being between ground and a corresponding one of the islands.
 15. The quantum register of claim 13, further comprising a second plurality of a single electron transistors, each single electron transistor in the second plurality being between islands in a corresponding pair of the islands.
 16. The quantum register of claim 15, further comprising a third plurality of single electron transistors, each single electron transistor in the third plurality being between ground and a corresponding one of the plurality of mesoscopic islands.
 17. A qubit, comprising: a first bank of a superconducting material having a first crystal orientation; a mesoscopic island having a second crystal orientation formed adjacent to the first bank; and a clean Josephson junction formed between the first bank and the mesoscopic island, wherein the first crystal orientation and the second crystal orientation are different wherein at least one of the mesoscopic island and the first bank comprises a d-wave superconducting material.
 18. The qubit of claim 17, further including a grounding mechanism coupled between the mesoscopic island and a ground.
 19. The qubit of claim 18, wherein the grounding mechanism is a single electron transistor.
 20. The qubit of claim 18, wherein the grounding mechanism is a parity key.
 21. The qubit of claim 17, wherein the clean Josephson junction includes a grain boundary between the island and the first bank.
 22. The qubit of claim 17, wherein the clean Josephson junction includes a normal metal.
 23. The qubit of claim 17, further comprising: a second bank of superconducting material having a third crystal orientation; and a Josephson junction formed between the first bank and the second bank.
 24. The qubit of claim 23, further comprising: a coupling mechanism coupled between the mesoscopic island and the second bank.
 25. The qubit of claim 24, wherein the coupling mechanism includes a single electron transistor.
 26. The qubit of claim 24, wherein the coupling mechanism includes a parity key.
 27. A quantum register, comprising: a first bank of superconducting material; at least one mesoscopic island of a superconducting material; and at least one clean Josephson junction, each clean Josephson junction in said at least one clean Josephson junction formed between a mesoscopic island in the at least one mesoscopic island and the first bank, wherein at least one of the at least one mesoscopic island and the first bank comprises a d-wave superconducting material.
 28. The quantum register of claim 27, further including at least one first coupling mechanism, each of the at least one first coupling mechanisms coupling a corresponding one of the at least one mesoscopic islands to ground.
 29. The quantum register of claim 28, wherein said at least one first coupling mechanism includes a single electron transistor.
 30. The quantum register of claim 28, wherein said at least one first coupling mechanism includes a parity key.
 31. The quantum register of claim 27, wherein said at least one mesoscopic island includes a pair of mesoscopic islands that are coupled to each other by a second coupling mechanism.
 32. The quantum register of claim 31, wherein the second coupling mechanism includes a single electron transistor.
 33. The quantum register of claim 31, wherein the second coupling mechanism includes a parity key.
 34. The quantum register of claim 27, further including: a second bank of superconducting material; and a Josephson junction formed between the second bank and the first bank.
 35. The quantum register of claim 34, further including a third coupling mechanism coupled between a mesoscopic island in said at least one mesoscopic island and the second bank.
 36. The quantum register of claim 35, wherein the third coupling mechanism includes a single electron transistor.
 37. The quantum register of claim 35, wherein the third coupling mechanism includes a parity key.
 38. The structure of claim 1, wherein a qubit is formed by the first bank, the mesoscopic island and the clean Josephson junction, and wherein each quantum state on the qubit is characterized by a clockwise or a counterclockwise supercurrent that circulates in a plane in the vicinity of the clean Josephson junction.
 39. The quantum register of claim 8, wherein a plurality of qubits is formed by the plurality of mesoscopic islands, the bank, and the plurality of clean Josephson junctions, and wherein each quantum state on each respective qubit in said plurality of qubits is characterized by a clockwise or a counterclockwise supercurrent that circulates in a plane in the vicinity of the Josephson junction in said respective qubit.
 40. The qubit of claim 17, wherein each quantum state, on the qubit is characterized by a clockwise or a counterclockwise supercurrent that circulates in a plane in the vicinity of the clean Josephson junction.
 41. The quantum register of claim 27, wherein a qubit is formed by each mesoscopic island in the at least one mesoscopic island together with the first bank and a Josephson junction in the at least one Josephson junction, and wherein each quantum state of each said qubit is characterized by a clockwise or a counterclockwise supercurrent that circulates in a plane in the vicinity of the Josephson junction in said qubit.
 42. The structure of claim 1, wherein a qubit is formed by the first bank, the mesoscopic island and the clean Josephson junction, and wherein the qubit has a quantum state that is twice degenerate in the absence of an external electromagnetic field.
 43. The quantum register of claim 8, wherein a plurality of qubits is formed by the plurality of mesoscopic islands, the bank, and the plurality of clean Josephson junctions, and wherein each qubit in said plurality of qubits has a quantum state that is twice degenerate in the absence of an external electromagnetic field.
 44. The qubit of claim 17, wherein the qubit has a quantum state that is twice degenerate in the absence of an external electromagnetic field.
 45. The quantum register of claim 27, wherein a qubit is formed by each mesoscopic island in the at least one mesoscopic island together with the first bank and a Josephson junction in the at least one Josephson junction, and wherein each said qubit has a quantum state that is twice degenerate in the absence of an external electromagnetic field.
 46. A qubit comprising: a first bank of a superconducting material having a first crystal orientation; a mesoscopic island of a superconducting material having a second crystal orientation, wherein at least one of the mesoscopic island and the bank comprises a d-wave superconducting material; a clean Josephson junction between the island and the bank, wherein the Josephson junction is configured so that a supercurrent proximate to the Josephson junction alternates between a first ground state having a first magnetic moment and a second ground state having a second magnetic moment by means of quantum tunneling; and circuitry to allow selective interruption of quantum tunneling between the first ground state and the second ground state.
 47. The qubit of claim 46, wherein the circuitry comprises a parity key that connects the island to ground.
 48. The qubit of claim 46, wherein the circuitry comprises a single electron transistor that connects the island to ground.
 49. A quantum computer comprising the qubit of claim 46 and a readout device for detecting whether the supercurrent has the first magnetic moment or the second magnetic moment.
 50. A quantum register comprising: a bank of a superconducting material; a plurality of mesoscopic islands of superconducting material; a plurality of clean Josephson junctions, wherein each respective Josephson junction: is between the bank and a corresponding one of the islands; and is configured so that a supercurrent proximate to the respective Josephson junction alternates between a first ground state having a first magnetic moment and a second ground state having a second magnetic moment; and circuitry to allow selective interruption of the alternating between the first ground state and the second ground state of the supercurrent associated with each Josephson junction, and wherein at least one of the plurality of mesoscopic islands and the bank comprises a d-wave superconducting material.
 51. A quantum computer comprising the quantum register of claim 50 and a readout device for detecting whether the supercurrent of each clean Josephson junction has the first magnetic moment or the second magnetic moment. 